Current Affairs 8th Class

Data Handling

Data Handling   Statistics is the formal science of making effective use of numerical data relating to group of individuals or experiments. It deals with all aspects, including the collection, analysis and interpretation of data and also the planning of the collection of data in terms of the design of surveys and experiments. A statistician is someone who is particularly versed in the ways of thinking necessary for the successful application of statistical analysis. Often such people have gained this experience after starting work in number of fields. This is also a discipline called Mathematical Statistics, which is concerned with the theoretical basis of the subject.   Types of Data The data may be in the form of raw or grouped. The data which is not arranged in any form is known as the raw data and data which is arranged in a definite pattern is known as the grouped data.is normally classified into two types. Primary data and Secondary data. The primary data is that data which is collected by the person himself for his own personal use, while secondary data is that data which is collected by others and used by someone else for his or her use. It may be data collected form the books, newspaper internet or any other sources.   Pie Chart A pie chart is the pictorial representation of the given data with the help of non-intersecting sectors of different areas and different central angles. The magnitude of the central angles depend on the magnitude of the data. In a pie chart, the arc length of each sector and consequently its central angles and area, is directly proportional to the quantity it represents. It is named for its resemblance to a pie which has been sliced. The following pie chart represent the population of English native speakers in different countries.   Co-ordinates of a Point                                        The pair of points which is used to describe the location of a point in two dimensional system are called co-ordinates of a point. The x-coordinate of a point is horizontal distance of the point from origin and y-coordinate of the point is the vertical distance from the origin.                                                              Line Graph                                                   A line graph is very useful for displaying data or information which changer continuously over a certain period of time. A line graph compares two variables. One variable is plotted along x-axis while another variable is plotted along y-axis.   Linear Graph                                                 A linear graph is a graph which is used to represent the linear relationship between two variables. To draw a linear graph we use co-ordinates along x and y axis. The difference between a line graph Or linear graph is that a line graph display information as a series of points joined by line segments while a linear graph is always a straight line.
• Example:
The quantity of petrol filled in a can and the cost of more...

Mensuration

Mensuration   His chapter deals with the concept of finding the surface area and volume of the regular figures. By regular figures we mean to say the figures whose parameters are known to us. Previously we have learnt to find the perimeter and area of the rectilinear figures, but now onwards we will learn to find the area of some polygons and also discuss the surface area and volume of some solid shapes namely cuboid cube, cone and cylinder.                                                  Area of a Polygon                                           Area of a given polygon can be found by dividing the given polygon into non-over lapping rectilinear figures. The area of the polygon will be equal to the sum of the areas of non-overlapping figures.
• Example:
Find the area of the polygon given below if AP = 10 cm, BP = 20 cm, CP = 50 cm, DP = 60 cm and PS = 90 cm   (a) $4080\,c{{m}^{2}}$           (b) $5050\,c{{m}^{2}}$ (c) $6060\,c{{m}^{2}}$           (d) $7070\,c{{m}^{2}}$ (e) None of these                                                       Answer (b)                                             Explanation: Area of the given figure     $=\frac{1}{2}\times 30\times 10+\frac{1}{2}\times 20\times 20+\frac{1}{2}\times 40(30+40)+\frac{1}{2}\times 40$$(20+60)+\frac{1}{2}\times 40\times 40\times \frac{1}{2}\times 60\times 30c{{m}^{2}}$ $=(150+200+1400+1600+800+900)c{{m}^{2}}$ $=5050c{{m}^{2}}$   Cuboid and Cube A cuboid is a closed rectangular solid bounded by six rectangular faces. A cuboid has 12 edges and 8 vertices. The length, breadth and height of a cuboid is generally denoted by I, b and h respectively. A cuboid whose length, breadth and height are equal is called a cube and each equal side is called edge of the cube.
• Example:
Determine the time in which the level of the water in a rectangular tank which is 50 m long and 44 m wide will rise by 7 cm if water is flowing through a cylindrical pipe of radius 7 cm at the rate of 5 kilometre per hour. (a) 4 hours                     (b) 3 hours (c) 2 hours                     (d) 5 hours (e) None of these   Answer (c) Explanation: Let x hours be the time taken by volume of water flowing through the pipe. Then, $\frac{22}{7}\times {{\left( \frac{7}{100} \right)}^{2}}\times 5000\times X$ $=\frac{22}{7}\times \frac{7}{100}\times \frac{7}{100}\times 5000X$ $=77x{{m}^{3}}$ Volume of tank $=\frac{50\times 44\times 7}{100}{{m}^{3}}=154{{m}^{3}}$ Therefore, $77x=154\Rightarrow x=2hours$   Cone and Cylinder Cone is a solid form which is generated by the revolution of a right angled triangle about one of the sides adjacent to the right angle. The base of a cone is always circular. While a cylinder has two identical circular ends and one curved surface and area of each circular ends are same.
• Example:
The volume of a cylinder having a height of 14 m and base radius 3 m is: (a)$792\,\,{{m}^{3}}$                         (b) $99\,\,{{m}^{3}}$ (c) more...

Geometry

Geometry   Polygon Any figure bounded by three or more line segments is called a polygon. A regular polygon is one in which all sides are equal and all angles are equal. A regular polygon can be inscribed in a circle. The name of polygons with three, four, five, six, seven, eight, nine and ten sides are respectively triangle, quadrilateral, pentagon, hexagon, heptagon, octagon, nonagon and decagon.   Convex Polygon In a convex polygon, a line segment between two points on the boundary never goes outside the polygon. More precisely, in a convex polygon no internal angle can be more than$180{}^\circ$.   Convex polygon   Concave Polygon In a concave polygon, a line segment between two points on the boundary goes outside the polygon. or In a concave polygon atleast one of the interior angle is more than$180{}^\circ$.   Concave polygon   Some important Formulae (i) Sum all the angles in a convex polygon is$(2n-4)90{}^\circ$. (ii)Exterior angle of a regular polygon is$\frac{360{}^\circ }{n}$. (iii)Interior angle of a regular polygon is$\left( 180{}^\circ -\frac{360{}^\circ }{n} \right),$ where n is number of sides of the polygon (iv) Number of diagonals of a convex polygon of n sides is$\frac{n\left( n-3 \right)}{2}$.   Quadrilaterals A plane closed figured bounded by four segments is called quadrilateral.
• The sum of four angles of a quadrilateral is equal to$360{}^\circ$.
• If the four vertices of a quadrilateral lie on the circumference of a circle i.e. if the quadrilateral can be inscribed in a circle it is called a cyclic quadrilateral. In a cyclic quadrilateral, the sum of opposite angles $=180{}^\circ$, i.e. $A+C=180{}^\circ$and $B+D=180{}^\circ$                                                                                        Parallelogram                                                   A quadrilateral having opposite sides are parallel is called a parallelogram. In a parallelogram, (i) opposite sides are equal.                                                   (ii) opposite angles are equal.                                                  (iii) each diagonal divides the parallelogram into two congruent triangles.          (iv) sum of any two adjacent angles is$180{}^\circ$. (v) the diagonals bisect each other.                                                                              Rhombus                                           A parallelogram is a rhombus is which every pair of adjacent sides are equal (all four sides of a rhombus are equal).     Since, a parallelogram is a rhombus, all the properties of a parallelogram apply to a rhombus. Further, in a rhombus, the diagonals are perpendicular to each other.   Rectangle                                                    A parallelogram is a rectangle in which each of the angles is equal to$90{}^\circ$. The diagonals of a rectangle are equal. A rectangle is also a special type of parallelogram and hence all properties of parallelogram apply to rectangles also.   Square A rectangle is a square in which all four sides are equal (a rhombus in which all more...

Comparing Quantities

Comparing Quantities   Variations If two quantities are related with each other in such a way that change in one quantity will produce the corresponding change in the other quantity then they are said to be in variations. The variation may be that if we increase or decrease the one quantity then other quantity may also increase or decrease and vice-versa. If increase in one quantity results in the corresponding increase or decrease in other quantity then it is called direct variation and if increase in one quantity will result in to decrease in other quantity or vice-versa then it is called indirect variation. For example increase in the cost with the increase in quantity is a direct variation whereas decrease in the time taken for a work with increase in the number of workers is an inverse variation.   Direct variation Two quantities are said to varies directly if increase in one quantity will results the increase in other or decrease in one quantity will results the decrease in other quantity In other words if two quantities are in direct variation, then they are said to be directly proportional to each other.   Following are some examples of direct variations:
• The cost of articles varies directly as the number of articles increases.
• The distance covered by a moving object varies directly as its speed increases or decreases. (It means if speed increases then the more distance covered in the same time).
• The work done varies directly as the number of men increases.
• The work done varies directly as the working time increases.

• Example:
A car travels 225 km with 15 litre of petrol. How many litre of petrol are needed to travel 135 km? (a) 6 litres                      (b) 9 litres       (c) 10 litres                    (d) 12 litres        (e) None of these                                                         Answer (b)                                                            Explanation: Petrol required to cover a distance of 225 km = 15 litres   Petrol required to cover a distance of 1 km  $=\frac{15}{225}$litres                    Petrol required to cover a distance of 135 km =$\frac{15}{225}\times 135=9$litres   Inverse variation Two quantities are said to be in inverse variation if increase in one quantity results in decrease in the other quantity and vice versa. Following are some examples of inverse variations: The time taken to finish a piece of work varies inversely as the number of men at work varies, (more men take less time to finish the job and less men will take more time) The speed varies inversely to the time taken to cover a given distance (more is the speed less is the time taken to cover a distance. The number of hours it takes for a block of ice to melt varies inversely to the temperature.
• Example:
A certain project can be completed by 5 workers in 24 days. How many workers are needed to finish the project in 15 days? (a) more...

Algebra

Algebra   An algebraic expression is an expression in one or more variables having different number of terms. Depending on the number of terms it may be monomials, binomials or polynomials. Like in the case of real numbers we can also Use different mathematical operations on algebraic expression. Previously we have learnt to add and subtract the algebraic expression. In this chapter we will learn, how to multiply or divide the algebraic expression. We will also learn how to find the linear factors of the algebraic expression as in the case of real numbers and how to form a linear equation in one variable and to find its solution.   Multiplication of Algebraic Expressions When two algebraic expressions are multiplied, the result obtained is called the product. The expressions being multiplied are called factors or multiplicands. While multiplying algebraic expressions first multiply numerical coefficients, then list all the variables that occur in the terms being multiplied and add the exponents of like variables.
• Example:
Find the product of $(2{{x}^{2}}-5x+4)$ and $({{x}^{2}}+7x-8)$. (a) $(2{{x}^{4}}-9{{x}^{3}}-47{{x}^{2}}+68x+32)$ (b) $(2{{x}^{4}}+9{{x}^{3}}-47{{x}^{2}}+68x-32)$ (c) $(2{{x}^{4}}-9{{x}^{3}}-47{{x}^{2}}+68x-32)$ (d) $(2{{x}^{4}}-9{{x}^{3}}-47{{x}^{2}}-68x-32)$ (e) None of these Answer (b)   Explanation: $(2{{x}^{2}}-5x+4)$$({{x}^{2}}+7x-8)$. $=2{{x}^{2}}({{x}^{2}}+7x-8)-5x({{x}^{2}}+7x-8)+4({{x}^{2}}+7x-8)$$=2{{x}^{4}}+14{{x}^{3}}-16{{x}^{2}}-5{{x}^{3}}-35{{x}^{2}}+40x+4{{x}^{2}}+$$28x-32$ $=2{{x}^{4}}+9{{x}^{3}}-47{{x}^{2}}+68x-32$   Division of Algebraic Expressions The process for division of algebraic expressions is similar to the multiplication process, the only difference is that in division process we have to divide the numerical coefficients and subtract the exponents instead of adding. The following points should be remembered while dividing algebraic expressions.
• If there are numerical coefficients in the expressions to be divided, just divide the numerical coefficient and then divide the variables by using the laws of exponents.
• To divide the variables just subtract the exponents of like variables.

• Example:
The simplest form of $\frac{9{{x}^{4}}{{y}^{7}}}{3{{x}^{2}}{{y}^{4}}}$ is: (a)$3xy$                                             (b)$3{{x}^{2}}{{y}^{2}}$ (c)$3{{x}^{2}}{{y}^{3}}$                                        (d) $3{{x}^{3}}{{y}^{3}}$ (e) None of these Answer (c) Explanation: $\frac{9{{x}^{4}}{{y}^{7}}}{3{{x}^{2}}{{y}^{4}}}=\left( \frac{9}{3} \right)({{x}^{4-2}})({{y}^{7-4}})=3{{x}^{2}}{{y}^{3}}$   Factorisation Factorisation of an algebraic expression is the process of writing the algebraic expression as a product of two or more linear factors. Each multiple of the algebraic expression is called factors of the algebraic expression. Thus the process of splitting the given algebraic expression into the product of two or more linear factors is called factorisation.   Factor Theorem According to the factor theorem if $f(x)$ is polynomial which is completely divisible by another polynomial$g(x)=x-a$, then $x-a$ is called the factor of the polynomial $f(x)$ and $f(a)=0$ for all values of$a$.   Methods of Factorisation Different algebraic expressions can be factorised by different methods. Monomials can be easily written into their linear factors. Binomials can be factorised by using identities which you have learnt in previous classes. The quadratic equation can be factorised by spliting the middle term and cubic equation can be factorised by first dividing it by linear factors and then reducing it to the quadratic form and then spliting the middle term. The other methods of factorisation are by grouping the terms having the common coefficients or having some common variables. more...

Conservation Plants and Animals

Conservation of Plants and Animals   Conservation It is the protection of natural resources like plants, animals, soil, water, fossil fuels etc. and the sustainable use of such resources. Natural resources are grouped into two categories: renewable resource is the one that may be replaced over the time by natural processes such as fish populations, natural vegetation or is inexhaustible such as the solar energy. Nonrenewable resources are those which are limited in supply and cannot be replaced even over extremely long period of time. The nonrenewable resources include fossil fuels and mineral deposits, such as iron ore and gold ore. Conservational activities for the nonrenewable resources focus on maintaining an adequate supply of these resources well in the future.                 Natural resources are conserved for their biological, economical and recreational values, as well as their natural beauty and importance to the local cultures. For example, tropical rainforests are protected for their important role in both the global ecology and the economic livelihood of the local culture. A coral reef may be protected for its recreational value for scuba divers and a scenic river may be protected for its natural beauty.   Biodiversity A wild range of different types of organisms which grow, multiply and thrive naturally, are found at any given time in a particular habitat. We should conserve forests and wildlife to preserve biodiversity to prevent endangered species from becoming extinct and to maintain ecological balance in nature.   Deforestation     Deforestation means large scale removal of forest prior to its replacement by other land uses Forests are removed for a variety of reasons, including agriculture, timber harvesting, mining and to make way for roads, dams and human settlements.   Protected Areas Protected areas are the areas of land or sea especially dedicated to the protection and maintenance of biodiversity. These are managed through legal means and have been set up within the legal frame work of Indian wildlife (Protection) Act.1972. Examples of protected areas are national parks and wildlife sanctuaries.   National Parks A national park is a large area dedicated to conserve the environment, natural resources and the wildlife therein. In a national park,
• Private rights are non-existent.
• Forestry operations, grazing of animals and hunting of animals are prohibited.
• Visitors are allowed to enter only for study, cultural and re-creative purposes.
• Exploitation of habitat or wildlife is banned.
Wildlife Sanctuaries
• A wildlife sanctuary is similar to a national park. However, it aims only at conservation of species. The wildlife sanctuaries have the following features:
• The boundary of a sanctuary is not limited by state legislation.
• The killing, hunting or capturing of any species is prohibited.
• Private ownership may be allowed to continue in a sanctuary.
• Forestry and other usages may be permitted, but to the extent that they do not affect wildlife adversely.
Forest Reserves These more...

Pollution of Air and Water

Pollution of Air and Water   Pollution Our environment is our surrounding. It comprises all living and nonliving things. Any undesirable change in the physical, chemical or biological characters of air, water and soil leads to environmental pollution which is harmful to human beings directly or indirectly.   Pollutant A pollutant is a substance that may be added to the environment directly or indirectly by man or natural events, to an extent which adversely affects humans, animals, vegetation and other materials.   Air Pollution Air pollution is defined as the addition of undesirable materials into the atmosphere either due to human activities which adversely affect the quality of the air and hence life on earth or through natural process like volcanic eruption.   Causes of Air Pollution
 1 Human activities 2 Thermal power plants 3 Burning of fossil fuels 4 Motor vehicles 5 Industries 6 Volcanic eruption
Greenhouse Effect Greenhouse effect may be defined as a phenomenon that enables the earth's atmosphere to trap the heat from the sun and prevent it from escaping into the outer space, there by warming the earth's surface.   Acid Rain The burning of fossil fuels containing sulphur, nitrogen and carbon produces acidic oxides of these elements. Carbon dioxide, an oxide of carbon, dissolves in water droplets to produce carbonic acid (a weak acid). The oxides of sulphur and nitrogen react with water to form sulphuric acid more...

Solar System and Some Natural Phenomenon

Solar System and Some Natural Phenomenon   Solar System Solar system, the sun and everything that orbits the sun, including the planets and their satellites the dwarf plants, asteroids, kuiper belt objects and comets.     Sun Solar is the closest star to the earth. Its average distance from the earth is about 150 million kilometers. It consists mainly of hydrogen and helium. Diameter of sun is about 1.4million km. The temperature at its surface is about$6000{}^\circ C$.   Planets Based on the distances of planets from the sun they are as follows: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus and Neptune. All the planets revolve around the sun in a fixed path called orbit. Planets which are close to the sun like Mercury, Venus, Earth and Mars are called inner planets or terrestrial planets. Jupiter, Saturn, Uranus and Mars are known as the outer planets or jovian planets as they are far from the sun.
• Mercury- is nearest to the sun. This planet has a rocky surface which is covered with craters. It is the smallest planet of the solar system.

• Venus- is the second planet from the sun. Venus is a rocky planet. It is the hottest planets as its atmosphere is mainly made up of carbon dioxide. It rotates on its axis from east to west.

• Earth - is the third planet from the sun. Earth's atmosphere has sufficient oxygen, the gas we need to live and water.

• Mars - is also known as a red planet. The thin atmosphere of mars contains mainly carbon dioxide with small amounts of nitrogen, oxygen, noble gases and water vapour. It appears red due to the high amount of iron oxide present on its surface.

• Jupiter - is the biggest planet and is made mainly of hydrogen and helium.

• Saturn - is the second biggest planet of the solar system and is made up of mainly hydrogen and helium. It has well developed system of rings surrounding it. It is the least dense planet and can float in water.
• Uranus - is the third biggest planet of the solar system and is mainly made up of hydrogen and helium.

• Neptune - is the outermost planet of the solar system and is made mainly of liquid and frozen hydrogen and helium gases.
The Moon A celestial body that revolves around a planet is known as natural satellite or moon of the planet. The earth has only one moon. It reflects the light of the sun. Its surface is covered with craters and mountains.    Phases of moon Shapes of the bright part of the moon, as seen from the earth, are known as the phases of moon.     Constellations Are group of stars which appear to form some recognizable more...

Chemical Effects of Current and Light

Chemical Effects of Current and Light   Chemical reactions are caused by passing of electric current through a conducting solution. This is called chemical effect of electric current.   Electric Current An electric current is a movement of charge. When two objects with different charges come in contact with each other and redistribute their charges, an electric current flows from one object to the other until the charge is distributed according to the capacities of the objects. If two objects are connected by a material that lets charge flow easily, such as a copper wire, then an electric current flows from one object to the other through the wire. Electric current is measured in ampere.   Conduction of Electric Current Through Liquids A solution of a substance or a substance in a liquid state which can conduct electricity is called an electrolyte. Most liquids that conduct electricity are solutions of acids, bases and salts. The Chemical decomposition of an electrolyte on passing an electric current through it is called electrolysis. Electrolysis is used very widely in industries like electroplating of metals, refining of copper and extraction of aluminum from ore. To make electrolysis happen there require two conductors cathode (-) and anode (+).     Electroplating The process of covering a more reactive metal with a less reactive metal with the help of electricity is known as electroplating. Material to be plated should be connected as cathode while anode usually loses material.   Light The sense of sight is one of the most important senses. Through this we see things around as. Light is an electromagnetic radiation, specifically radiation of a wavelength that is visible to the human eye.   Luminous and Non-luminous Objects
• The objects which emit their own light are called luminous objects. For example, sun, stars, electric bulb, glowing tube light, torch, etc.
• The objects which do not emit their own light are called non-luminous objects. For example, the moon, earth, table, chair, book, trees, etc.
Reflection of Light Is the phenomenon of sending back light rays which fall on the surface of an object.     Laws of reflection According to first law of reflection: the incident ray, the reflected ray and the normal ray, all lie in the same plane. According to second law of reflection: the angle of incidence is always equal to angle of reflection.   Periscope Is a long, tubular device used to observe over, around or through an object that is out of direct line of sight. A periscope works on the reflection of light from two plane mirrors arranged parallel to one another.   Human Eye The eye enables us to see the various objects around us. The main parts of human eye are:
• Cornea - is the front part of the eye which is made more...

Force, Friction and Sound

Force, Friction and sound   Force A force is a push or pull. The direction in which an object is pussed or pulled is called the direction of the force. Whenever there is an interaction between two objects, there is a force acting on each of the objects. Forces acting between objects can be placed into two categories:   Contact Forces Are those types of forces which result when the two interacting objects are perceived to be physically contacting each other.   Types of Contact Forces
• Muscular Force - is the force exerted by the muscles of the body. This force can be applied to an object only when our body is in contact with the object, therefore muscular force is a contact force.
• Frictional Force - is the force which opposes the motion of one body over another body.
Non-contact Forces Are those forces which result when the two interacting objects are not in physical contact with each other.   Types of Non-contact Forces
• Gravitational Force - is the force by which all things with mass are brought toward one another. It is the gravitational force between the sun and the earth which holds the earth in its orbit around the sun.
• Magnetic Force - is the force exerted by a magnet. The magnetic force between two magnets placed near one another can be that of "attraction" or "repulsion” depending upon which poles of the two magnets are facing each other.
• Electrostatic Force - is the force exerted by an electrically charged object.
Pressure Pressure, in mechanics is the force per unit area exerted by a liquid or gas on a body surface, with the force acting at right angles to the surface uniformly in all directions. Mathematically: p = Where P is the pressure, F is the normal force and A is the area. Unit of pressure is Pascal or$N/{{m}^{2}}$   Atmospheric Pressure This pressure exerted by the atmosphere is called atmospheric pressure. It decreases with increase in height.   Friction Friction is the force that opposes the motion of an object when the object is in contact with another object or surface. Friction results from two surfaces rubbing against each other or moving relative to one another. It can hinder the motion of an object or prevent an object from moving at all. The strength of frictional force depends on the nature of the surfaces that are in contact and the force pushing them together.   Causes of Friction Friction occurs because rough surfaces tend to catch on one another as they slide past each other. Even surfaces that are apparently smooth can be rough at the microscopic level. They have many ridges and grooves. The ridges of each surface can get stuck in the grooves of the other, effectively creating a type of mechanical bond or glue, between the surfaces.   Kinds of Friction
• Static Friction - the frictional force acting between the two more...

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